The origin of multiple clustering behaviors in superconformal minimal models

The bulk-boundary correspondence is a robust and essential feature of many topological phases of matter which relates bulk wavefunctions to correlation functions of the edge conformal field theory. One prominent set of examples are the Read-Rezayi series of quantum Hall states. Their wavefunctions (correlators in edge CFT) are well captured by Jack polynomials which encode clustering behaviors of particles approaching each other. In this work, we investigate wavefunctions of topological phases corresponding to the N=1 superconformal minimal model type. We present exact decompositions of supersymmetry generating operators into a sum of simpler operators with specific clustering behaviors. In this way, their 2n-point wavefunctions(correlators) can be computed from ground up using these building blocks. Our results provide an intuitive understanding of clustering behaviors and internal structures of these wavefunctions(correlators). Extensions to other superconformal minimal models are also discussed.